Method for Combating Impulsive Interference/Noise in Multicarrier Underwater Acoustic Communications

ABSTRACT

A communication system includes a repetitive orthogonal frequency-division multiplexing (“ROFDM”)transmitter communicating with an ROFDM receiver. The ROFDM transmitter includes an ROFDM modulator, which includes a K-point Fast Fourier Transform receiving a block of time-domain data symbols and generating an initial orthogonal frequency-division multiplexing symbol. The initial orthogonal frequency-division multiplexing symbol is based on a block of frequency-domain data symbols corresponding to the block of time-domain data symbols. The initial orthogonal frequency-division multiplexing symbol includes an ending part. The ROFDM modulator includes an orthogonal frequency-division multiplexing symbol repeater generating a repetitive orthogonal frequency-division multiplexing symbol by repeatedly reproducing the initial orthogonal frequency-division multiplexing symbol. The modulator includes a cyclic prefix adder pretending a cyclic prefix to the repetitive orthogonal frequency-division multiplexing symbol to generate a baseband transmitted signal. The cyclic prefix includes the ending part of the initial orthogonal frequency-division multiplexing symbol. The ROFDM receiver includes an ROFDM demodulator.

CROSS-REFERENCE TO RELATED APPLICATIONS

The present application is a continuation of U.S. patent applicationSer. No. 16/247,626, which was filed on 15 Jan. 2019 and accordinglyclaims priority thereto.

BACKGROUND OF THE INVENTION Field of the Invention

This invention relates in general to a method for multicarrier acousticcommunications, and in particular to a method for multicarrierunderwater acoustic communications in the presence of at least a strongimpulsive noise.

Description of the Related Art

Multicarrier underwater acoustic communications has gained popularity inrecent years thanks to its provision of high bandwidth efficiency andlow system complexity. All current multicarrier underwater acousticcommunication systems have been designed with only the ambient noise inmind, and their performance suffers when a strong impulsive noise isalso present in the channel.

Such impulsive noise is common in coastal seas. Unlike the ambient noisethat are mostly caused by the shipping noise, surface wind and breakingwaves, the main source of the impulsive noise is the noise-generatingmarine life such as snapping shrimp. In an ocean environment abundant insuch marine life, the impulsive noise tends to be strong; having a highimpulse rate and a large impulse variance. The impulsive noise consistsof random pulses that are relatively short in the time domain but verybroad in the frequency domain. Previous analysis has shown that theimpulsive noise, when strong, is particularly damaging to multicarriercommunications where data symbols are carried in the frequency domain.For multicarrier modulation such as orthogonal frequency divisionmultiplexing (“OFDM”), the corresponding demodulation operation spreadsout the effect of the impulsive noise across the entire bandwidth. Whenthe impulsive noise is strong, this could drastically impact every datasymbol within the bandwidth, and cause more errors than what classicchannel coding can handle. Two approaches are commonly used to combatthe impulsive noise: 1) random pulse localization and removal; and 2)Reed-Solomon decoding.

Random Pulse Localization and Removal

The signal processing approach involving random pulse localization andremoval amounts to first locating the random pulses in the receivedsignal and then removing them prior to signal recovery. This approachexploits characteristic differences between the communication signal andthe impulsive noise, and it is effective if and only if the impulsivenoise can be distinguished from the communication signal. Therefore,this approach does not suit well for multicarrier communications becausemulticarrier communication signals are generally impulse-like.

Reed-Solomon (RS) Decoding

The Reed-Solomon (RS) decoding coding approach exploits the similaritybetween OFDM modulation and RS coding to mitigate the impulsive noise bytreating random pulses as channel-induced errors. However, due to thelimited error-correction capability, this approach has been shownineffective when the impulse rate is high.

BRIEF SUMMARY OF THE INVENTION

An embodiment of the invention includes a communication system. Thecommunication system includes a repetitive orthogonal frequency-divisionmultiplexing transmitter and a repetitive orthogonal frequency-divisionmultiplexing receiver communicating with the repetitive orthogonalfrequency-division multiplexing transmitter.

Optionally, the transmitter includes a repetitive orthogonalfrequency-division multiplexing modulator. The repetitive orthogonalfrequency-division multiplexing modulator includes a K-point FastFourier Transform receiving a plurality of time-domain data symbols andgenerating an initial orthogonal frequency-division multiplexing symbol.The initial orthogonal frequency-division multiplexing symbol is basedon a plurality of frequency-domain data symbols corresponding to theplurality of time-domain data symbols. The initial orthogonalfrequency-division multiplexing symbol includes an ending part. Therepetitive orthogonal frequency-division multiplexing modulator includesan orthogonal frequency-division multiplexing symbol repeater receivingthe initial orthogonal frequency-division multiplexing symbol from theK-point Fast Fourier Transform and generating a repetitive orthogonalfrequency-division multiplexing symbol by repeatedly reproducing theinitial orthogonal frequency-division multiplexing symbol. Therepetitive orthogonal frequency-division multiplexing modulator includesa cyclic prefix adder receiving the repetitive orthogonalfrequency-division multiplexing symbol from said orthogonalfrequency-division multiplexing symbol repeater and generating abaseband transmitted signal by prepending a cyclic prefix to therepetitive orthogonal frequency-division multiplexing symbol, the cyclicprefix comprising the ending part of the initial orthogonalfrequency-division multiplexing symbol.

Optionally, the receiver further includes a repetitive orthogonalfrequency-division multiplexing demodulator. The repetitive orthogonalfrequency-division multiplexing demodulator includes a signalpartitioner receiving the baseband received signal from the carrierdemodulator. The signal partitioner divides the baseband received signalinto a plurality of received sub-signals. The repetitive orthogonalfrequency-division multiplexing demodulator includes a noise stateclassifier receiving the plurality of received sub-signals from thesignal partitioner, and generating a plurality of noise-state index setsindexing at least one time instant at which each sub-signal of theplurality of sub-signals is free of the random impulses. The repetitiveorthogonal frequency-division multiplexing demodulator includes atime-dependent selective combiner receiving the plurality of receivedsub-signals from the signal partitioner and the plurality of noise-stateindex sets from the noise state classifier. The time-dependent selectivecombiner combines the plurality of sub-signals selectively according tothe noise-state index sets thereby generating a received orthogonalfrequency-division multiplexing symbol signal free of impulsive noise.The repetitive orthogonal frequency-division multiplexing demodulatorincludes an orthogonal frequency division multiplexing symbol detectorreceiving the received orthogonal frequency-division multiplexing symbolsignal from the time-dependent selective combiner and decoding theplurality of time-domain data symbols from the received orthogonalfrequency-division multiplexing symbol signal.

An embodiment of the invention exhibits high robustness against theimpulsive noise. Thanks to ROFDM modulation, the ROFDM receiver is ableto completely eliminate the effects of the impulsive noise on symbolrecovery. Therefore, its performance is extremely robust against theimpulsive noise. ROFDM is well suited for the sea environment withdominant impulsive noise.

An embodiment of the invention exhibits controllable reliability againstthe ambient noise. In ROFDM, the amount of the processing gain that canbe achieved is determined by the number of repetitions. By choosing aproper number of repetitions, ROFDM is thus capable of guaranteeingreliable symbol recovery even if the received SNR is low. This makes itparticularly attractive for the case where the system can only afford asingle source and a single receiver.

An embodiment of the invention exhibits low system complexity. At theROFDM receiver, neither signal partition nor noise-state classificationrequires much computation. And, symbol recovery can be implemented byusing fast Fourier transform. Furthermore, similar to classic OFDM, nocomplicated channel estimation and equalization is needed. Overall,ROFDM enjoys extremely low computational complexity. As a result, anembodiment of the ROFDM system can be implemented at low cost.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a block diagram of an embodiment of a communication systemaccording to the instant invention.

FIG. 2 is a block diagram of an embodiment of a transmitter in acommunication system according to the instant invention.

FIG. 3 is a block diagram of an embodiment of a receiver in acommunication system according to the instant invention.

FIG. 4 is a block diagram of an illustrative baseband transmitted signalgenerated by an embodiment of the invention.

DETAILED DESCRIPTION OF TH E INVENTION

An embodiment of the invention includes a repetitive orthogonalfrequency-division multiplexing (“ROFDM”) communication system 10, asshown by way of illustration in FIG. 1. The communication system 10includes an ROFDM transmitter 20, as shown by way of illustration inFIGS. 1 and 2. The ROFDM transmitter 20 includes an ROFDM modulator 30.The ROFDM modulator 30 includes a standard K-point Fast FourierTransform 40 receiving a block of time-domain data symbols andgenerating an initial orthogonal frequency-division multiplexing(“OFDM”) symbol. The initial OFDM symbol is based on a block offrequency-domain data symbols corresponding to the block of time-domaindata symbols. The ROFDM modulator 30 further includes a standard OFDMsymbol repeater 50 generating an ROFDM symbol by repeatedly reproducingthe initial OFDM symbol. The ROFDM also includes a standard cyclicprefix adder 60 prepending a cyclic prefix to the ROFDM symbol togenerate a baseband transmitted signal. The cyclic prefix includes theending part of the initial OFDM symbol. FIG. 4 shows an illustrativebaseband transmitted signal 100. FIG. 4 shows a cyclic prefix 110 andonly three repeated initial OFDM symbols 120 for ease of illustrationand understanding. In general, a minimum of two repeated initial OFDMsymbols are required for one ROFDM symbol, and more initial OFDM symbolsfoster better symbol recovery in the presence of ambient and impulsivenoise in the transmission medium (e.g., an undersea channelenvironment). However, one of ordinary skill in the art will readilyappreciate that there is a tradeoff between bandwidth efficiency andperformance against impulsive noise.

Optionally, the ROFDM transmitter 20 further includes a standard channelencoder 70 receiving an input signal. The input signal includes aplurality of information bits. The channel encoder 70 generates theplurality of time-domain data symbols by adding redundancy to theplurality of information bits, e.g., using standard block andconvolutional codes. The channel encoder 70 transmits the plurality oftime-domain data symbols to the ROFDM modulator 30. Optionally, theROFDM transmitter 20 further includes a standard carrier modulator 80receiving the baseband transmitted signal from the ROFDM modulator 30,shifting the baseband transmitted signal to a proper passband, andtransmitting a passband transmitted signal.

The ROFDM communication system 10 further includes an ROFDM receiver 90communicating with the ROFDM transmitter 20, as shown by way ofillustration in FIGS. 1 and 3. The ROFDM receiver 90 includes a standardcarrier demodulator 130 receiving the passband transmitted signal,shifting the passband transmitted signal to a standard baseband, andgenerating a baseband received signal.

The ROFDM receiver 90 further includes an ROFDM demodulator 140receiving the baseband received signal from the carrier demodulator 100.The ROFDM demodulator 140 includes a standard signal partitioner 150receiving the baseband received signal from the carrier demodulator 130.The signal partitioner 150 divides the baseband received signal into aplurality of received sub-signals. The ROFDM demodulator 90 alsoincludes a noise state classifier 160. In an embodiment of theinvention, the noise state classifier 160 is implemented mainly insoftware. Illustrative details of a noise state classification algorithmtherefore are provided below. The noise state classifier 160 receivesthe plurality of received sub-signals from the signal partitioner 150and generating a plurality of noise-state index sets indexing at leastone time instant at which each sub-signal of the plurality ofsub-signals is free of the random impulses. The plurality of noise-stateindex sets is generated according to the noise state classificationalgorithm. The ROFDM demodulator 90 further includes a time-dependentselective combiner 170 receiving the plurality of received sub-signalsfrom the signal partitioner 150 and the plurality of noise-state indexsets from the noise state classifier 160. The time-dependent selectivecombiner 170 combines the plurality of sub-signals selectively accordingto the plurality of noise-state index sets thereby generating a receivedorthogonal frequency-division multiplexing symbol signal free ofimpulsive noise. The ROFDM demodulator 90 further includes a standardOFDM detector 180. The OFDM symbol detector 180 decodes the block of Ktime-domain data symbols from the received OFDM symbol signal togenerate channel-coded information bits and transmits same to a standardchannel decoder 190. The ROFDM receiver 90 further includes a channeldecoder 190. The channel decoder 190 in a standard manner removes theredundancy generated by the channel encoder 70 to recover the inputsignal including a plurality of information bits.

An embodiment of the invention is directed to a novel multicarriercommunication system 10, for example, tailored to a challenging underseachannel environment where a strong impulsive noise is present inaddition to the ambient noise. This channel environment, for example, istypical in coastal seas and has been observed in many shallow-water seaexperiments. An embodiment of the invention takes an approach differentfrom the two existing approaches discussed above in the Background ofthe Invention. Instead of relying solely on receiver processing tomitigate the impulsive noise, the multicarrier communication system 10according to an embodiment of the invention includes a cooperatingtransmitter and receiver. An embodiment of the invention is based upon anew multicarrier modulation scheme called ROFDM; ROFDM is a term of artfor the purpose of this patent application. ROFDM, for the purpose ofthis patent application, is described below with respect to componentsand operation of a transmitter and receiver according to one or moreembodiments of the invention.

The ROFDM Transmitter

At the ROFDM transmitter 20, according to an embodiment of invention,data symbols are transmitted in blocks of size K. The function of ROFDMmodulation is to map each block to an ROFDM signal prior totransmission. As depicted in FIGS. 1 and 2, the operation of (N,K)-ROFDMmodulation is composed of three successive steps: K-point Fast Fouriertransform (FFT), (N−1) repetitions, and cyclic prefix (“CP”) addition.The difference between (N,K)-ROFDM modulation and classic OFDM lies inthat classic OFDM includes no repetition. Therefore, ROFDM can be viewedas a generalized form of classic OFDM. Mathematically, a (N,K)-ROFDMsignal, for the purpose of this patent application, is expressed as:

$\begin{matrix}{{{u(t)} = {\sum\limits_{k = {- \frac{K}{2}}}^{\frac{K}{2} - 1}{a_{k}e^{j\; 2\pi \; k\; \Delta_{f}t}}}},{{- T_{cp}} < t < {NT}_{0}}} & (1)\end{matrix}$

where K is the number of subcarriers, a_(k)'s are information-bearingdata symbols, Δ_(f) denotes subcarrier spacing, T_(cp) is the durationof the CP and T₀ is the duration of one OFDM symbol. The signalingstructure of u(t) is shown by way of illustration in FIG. 4.

Just like (N,1)-repetition coding, the repetition in (N,K)-ROFDMdecreases the bandwidth efficiency by a factor of about N. While thisloss of bandwidth efficiency might seem significant, such repetition isdeemed necessary for the channel/noise environment (no transmitterarray, no receiver array, strong ambient/impulsive noise) this inventiontargets at. The repetition at the transmitter not only enables thereceiver to collect a processing gain in combating the ambient noisebut, more importantly, makes it possible for the receiver to locate andthen remove the impulsive noise prior to symbol recovery. As a result,much better system performance can be achieved, which in return can beused to trade back efficiency loss. This is in the same spirit ofchannel coding and spread spectrum technologies that have been widelyused for performance enhancement in challenging channel/noiseenvironments.

Noise/Data Model

An embodiment of the invention concerns the case where the noise iscomposite and contains the contribution from an impulsive noise and anambient noise. Mathematically, such noise is modeled as:

n(t)=w _(a)(t)+v(t)  (2)

where the ambient noise w_(a)(t) is a zero-mean Gaussian random processwith variance σ_(a) ², and the impulsive noise v(t) is a BernoulliGaussian random process:

v(t)=b(t)w _(i)(t)  (3)

with w_(i)(t) denoting a zero-mean Gaussian random process with varianceσ_(i) ²>>σ_(a) ², and b(t) an i.i.d. Bernoulli random process, taking avalue of “1” or “0” with probability p_(i) or (1−p_(i)), respectively.As per Equations (2) and (3), the noise n(t) must belong to one of twopossible states at any given time. The noise n(t) is said to be at the“high” state if n(t)=w_(a)(t)+w_(i)(t), and at the “low” state ifn(t)=w_(a)(t). The “high” and “low” states occur with probabilitiesp_(i) and (1−p_(i)), respectively, and are expected to be quite distinctbecause of σ_(i) ²>>σ_(a) ².

A standard single-input single-output (“SISO”) multipath channel betweenthe ROFDM transmitter 20 and the ROFDM receiver 90 is considered asfollows. Under the noise model of Equation (2), the received ROFDMsignal (after discarding the cyclic prefix) is expressed as

$\begin{matrix}{{{{r(t)} = {{x(t)} + {n(t)}}},{0 < t < {NT}_{0}}}{where}} & (4) \\{{{x(t)} = {\sum\limits_{k}{a_{k}H_{k}e^{j\; 2\pi \; k\; \Delta_{f}t}}}},{0 < t < {NT}_{0}}} & (5)\end{matrix}$

is the noise-fre received signal with H_(k) denoting the subchannel gainexperienced by the k-th subcarrier. A typical received ROFDM signalsuffers from a significant amount of the impulsive noise, and has arelatively low signal-to-noise ratio (“SNR”). For example, the impulsivenoise signal is multiples larger than the signal and may only last for afraction of a second.

The ROFDM Receiver

The ROFDM receiver 90 according to an embodiment of the inventionensures reliable symbol recovery from the received ROFDM signal when theambient noise and the impulsive noise are both strong. FIG. 3 shows anillustrative system diagram of the ROFDM receiver. In what follows, theoperation of its functional units are described.

Signal Partition

A unit of signal partition, or the signal partitioner 150, is used todivide the received signal r(t) into N signals r_(m)(t), m=1, . . . , N:

r _(m)(t)=x _(m)(t)+n _(m)(t),t∈[0,T ₀]  (6)

where r_(m)(t)=r(t+(m−1)T₀), x_(m)(t)=x(t+(m−1)T₀) andn_(m)(t)=n(t+(m−1)T₀). By using Equation (5), one property of the Nsignals r_(m)(t)'s is observed; their signal parts x_(m)(t)'s are allidentical. This important property is exploited to locate and remove theimpulsive noise prior to symbol recovery. It is worth pointing out thatthis property becomes available only when ROFDM modulation is employedat the transmitter.

Noise State Classification

A unit of noise state classification, or the noise state classifier 160,is used to classify the noise state of each of the N signals r_(m)(t)'sfor all time instants t. Recall that at any given time instant t,r_(m)(t)'s are supposed to be identical in the absence of the noise. Thenoise state classification of r_(m)(t) can be thus carried out by simplychecking whether r_(m)(t) is an outlier within the sample setR(t)={r₁(t), . . . , r_(N)(t)}. If it is, then r_(m)(t) is at the “highnoise” state; otherwise, it is at the “low noise” state. It is notedthat such noise state classification is impossible for classic OFDM. Toidentify outliers in the sample set R(t), the followinglargest-neighborhood (“LN”) algorithm is, for example, used:

-   -   Step 1. For a given t, compute N noise-state index sets        {l_(m)(t)}_(m=1) ^(N):

l _(m)(t)={j:∥r _(m)(t)− r _(j)(t)∥<ρ}

where the threshold ρ is determined by noise variances σ_(i) ² and σ_(a)².

-   -   Step 2. Pick the largest set (say, l(t)) among {l_(m)(t)}_(m=1)        ^(N). The noise-state index set I(t) contains indexes of those        signals in R(t) that have not been impacted by impulsive noise        for a given t.    -   Step 3. Repeat Step 1 and Step 2 until l(t) is found for all        time instants t∈[0, T₀].

Time-Dependent Selective Combining

A unit of time-dependent selective combining (“TDSC”), or time-dependentselective combiner 170, is used to mitigate both the impulsive noise andthe ambient noise prior to symbol recovery. The operation of thetime-dependent selective combiner 170 amounts to forming a combinedsignal y(t) as:

$\begin{matrix}{{y(t)} = {\frac{1}{{l(t)}}{\sum\limits_{m \in {I{(t)}}}{r_{m}(t)}}}} & (7)\end{matrix}$

where |l(t)| stands for the cardinality of the noise-state index setl(t) obtained via LN algorithm. As evident in (7), at any given time,the time-dependent selective combiner 170 only involves those receivedsignals that have been determined to be free of impulse noise at thattime. Because the noise state generally varies with time, thetime-dependent selective combiner 170 is thus both time-dependent andselective, as its name implies. By only involving received samples freeof impulse noise, the time-dependent selective combiner 170 is capableof eliminating the effects of the impulsive noise, while mitigatingthose of the ambient noise by offering a processing gain. Thetime-dependent selective combiner 170 has been proved optimal in thesense that it maximizes the SNR of y(t) among all linear combiningmethods.

OFDM Symbol Recovery

A unit of OFDM symbol detector 180 is used to recover data symbolsa_(k)'s from the combined signal y(t). By using Equations (5) and (6),y(t) in Equation (7) can be rewritten as:

$\begin{matrix}{{y(t)} = {\underset{\underset{signal}{}}{\sum\limits_{k}{a_{k}H_{k}e^{j\; 2\pi \; k\; \Delta_{f}t}}} + {w_{e}(t)}}} & (8)\end{matrix}$

where w_(e)(t) represents the effective noise after the time-dependentselective combiner 170. Because y(t) is nothing but the received signalof classic OFDM, one can thus recover data symbols using one of thosemany standard methods that have been designed for classic OFDM. Thisalso suggests that ROFDM is capable of preserving the most desirablefeatures of classic OFDM.

An embodiment of the invention comprises a computer programinstructions, which computer program instructions embody the steps,functions, filters, and/or subsystems described herein relative toiterative process for generating the highest-rated device response.However, it should be apparent that there could be many different waysof implementing the invention in computer programming, and the inventionshould not be construed as limited to any one set of computer programinstructions. Further, a skilled programmer would be able to write sucha computer program to implement an exemplary embodiment based on theappended diagrams and associated description in the application text.Therefore, disclosure of a particular set of program code instructionsis not considered necessary for an adequate understanding of how to makeand use the invention.

One of ordinary skill in the art will recognize that the methods,systems, and control laws discussed above may be implemented in softwareas software modules or instructions, in hardware (e.g., a standardapplication-specific integrated circuit (“ASIC”)), a standard fieldprogrammable gate array (“FPGA”), or in a combination of software andhardware. The methods, systems, and control laws described herein may beimplemented on many different types of processing devices by programcode comprising program instructions that are executable by one or moreprocessors. The software program instructions may include source code,object code, machine code, or any other stored data that is operable tocause a processing system to perform methods described herein.

The methods, systems, and control laws may be provided on many differenttypes of standard computer-readable media including standard computerstorage mechanisms (e.g., CD-ROM, diskette, RAM, flash memory,computer's hard drive, etc.) that contain instructions for use inexecution by a standard processor to perform the methods' operations andimplement the systems described herein.

The computer components, software modules, functions and/or datastructures described herein may be connected directly or indirectly toeach other in order to allow the flow of data needed for theiroperations. It is also noted that software instructions or a module canbe implemented for example as a subroutine unit or code, or as asoftware function unit of code, or as an object (as in anobject-oriented paradigm), or as an applet, or in a computer scriptlanguage, or as another type of computer code or firmware. The softwarecomponents and/or functionality may be located on a single device ordistributed across multiple devices depending upon the situation athand.

Systems and methods disclosed herein may use data signals conveyed usingnetworks (e.g., local area network, wide area network, internet, etc.),fiber optic medium, carrier waves, wireless networks, etc. forcommunication with one or more data-processing devices. The data signalscan carry any or all of the data disclosed herein that is provided to orfrom a device.

Although a particular feature of the disclosure may have beenillustrated and/or described with respect to only one of severalimplementations, such feature may be combined with one or more otherfeatures of the other implementations as may be desired and advantageousfor any given or particular application. Also, to the extent that theterms “including”, “includes”, “having”, “has”, “with”, or variantsthereof are used in the detailed description and/or in the claims, suchterms are intended to be inclusive in a manner similar to the term“comprising”.

This written description sets forth the best mode of the invention andprovides examples to describe the invention and to enable a person ofordinary skill in the art to make and use the invention. This writtendescription does not limit the invention to the precise terms set forth.Thus, while the invention has been described in detail with reference tothe examples set forth above, those of ordinary skill in the art mayeffect alterations, modifications and variations to the examples withoutdeparting from the scope of the invention.

These and other implementations are within the scope of the followingclaims.

What is claimed as new and desired to be protected by Letters Patent ofthe United States is:
 1. A communication system comprising: a repetitiveorthogonal frequency-division multiplexing transmitter; a repetitiveorthogonal frequency-division multiplexing receiver communicating withsaid repetitive orthogonal frequency-division multiplexing transmitter,wherein said transmitter comprises: a repetitive orthogonalfrequency-division multiplexing modulator comprising: a K-point FastFourier Transform receiving a plurality of time-domain data symbols andgenerating an initial orthogonal frequency-division multiplexing symbol,the initial orthogonal frequency-division multiplexing symbol beingbased on a plurality of frequency-domain data symbols corresponding tothe plurality of time-domain data symbols, the initial orthogonalfrequency-division multiplexing symbol comprising an ending part; anorthogonal frequency-division multiplexing symbol repeater receiving theinitial orthogonal frequency-division multiplexing symbol from saidK-point Fast Fourier Transform and generating a repetitive orthogonalfrequency-division multiplexing symbol by repeatedly reproducing theinitial orthogonal frequency-division multiplexing symbol; and a cyclicprefix adder receiving the repetitive orthogonal frequency-divisionmultiplexing symbol from said orthogonal frequency-division multiplexingsymbol repeater and generating a baseband transmitted signal byprepending a cyclic prefix to the repetitive orthogonalfrequency-division multiplexing symbol, the cyclic prefix comprising theending part of the initial orthogonal frequency-division multiplexingsymbol.
 2. The communication system according to claim 1, wherein saidtransmitter further comprises: a channel encoder receiving an inputsignal comprising a plurality of information bits, said channel encodergenerating the plurality of time-domain data symbols by addingredundancy to the plurality of information bits, said channel encodertransmitting the plurality of time-domain data symbols to saidrepetitive orthogonal frequency-division modulator.
 3. The communicationsystem according to claim 1, wherein said transmitter further comprises:a carrier modulator receiving the baseband transmitted signal from saidcyclic prefix adder, shifting the baseband transmitted signal to apassband, and transmitting a passband transmitted signal.
 4. Acommunication system according to claim 1 wherein said receiver furthercomprises: a carrier demodulator receiving a passband received signal,shifting the passband received signal to a baseband, and generating abaseband received signal.